Thursday, November 27, 2014

Do Numbers Evolve? (5)

I will attempt here to provide additional clarification on the holistic - as opposed to the standard analytic - interpretation of number.

Once again analytic interpretation is by its very nature linear (i.e. 1-dimensional) thus enabling numbers to be interpreted with respect to their reduced quantitative values.
This entails interpretation  with single polar reference frames (e.g. as unambiguously objective) in an independent absolute manner.

Thus with 1-dimensional interpretation (i.e. single poles of reference) dynamic interdependence (resulting from the interaction of more than one pole) cannot properly be interpreted and is thereby reduced in an independent manner.

Therefore at a minimum we require at least two interacting polar frames of reference to establish genuine interdependence. And in short holistic appreciation relates to the explicit recognition of the nature of such interdependence.

Now all holistic interdependence necessarily starts with the initial recognition of independence (which is conscious posited as the 1st dimension).

However 2-dimensional appreciation combines this 1st dimension (entailing analytic type appreciation) with a second dimension that entails the negation (of what has been posited).

Now this in fact is deeply relevant to the multiplication of two numbers.

In standard analytic terms when we multiply - say - 3 * 5, the answer is given in a reduced 1-dimensional fashion as 15 (i.e. 151). However a simple geometrical representation of this relationship will suggest that through multiplication the nature of the units has changed from linear (1-dimensional) to square (2-dimensional) format.

Thus there is something fundamentally missing from the conventional mathematical treatment of multiplication.

So when we probe more deeply into the nature of this simple operation (i.e. 3 * 5) we find that it cannot be properly explained in the absence of both the quantitative notion of independence and the qualitative notion of interdependence respectively.

So imagine 5 units laid out in 3 separate rows (in a rectangular fashion)! Now this implies that we recognise each unit in a (separate) independent fashion. However to then multiply by 3 we must also recognise that the units in each row share a common identity (thus enabling each row to placed in correspondence  with each other).

Now this recognition of interdependence (in a mutual shared identity of each unit) literally entails the (temporary) negation with respect to the (conscious) recognition of a posited independent identity.

Thus the qualitative recognition of a shared identity (through negation of each separate unit) in fact implies the 2nd dimension of understanding in this case.

Thus a comprehensive appreciation of  the multiplication of 3 * 5 entails recognition of the quantitative independence of each individual unit with the qualitative interdependence of all units (i.e. as sharing a common quality).

So comprehensive appreciation is here 2-dimensional, entailing a 1st dimension (relating to independent recognition) and a 2nd dimension (relating to qualitative interdependence in a mutual common recognition).

Now if we were to now properly explain - say - 3 * 5 * 4, this would entail 3-dimensional interpretation. So once again the 1st dimension would relate to the standard analytic appreciation of 60 independent units. However we would now have two layers of interdependence to appreciate. So for example if we arranged 5 units each in 3 rows on a bottom layer, this would entail - as before - the 1st level of interdependence. Then we would could lay each of these rectangles four units high creating a second compounded level of interdependence.

Now remarkably the various roots of 1 (when appropriately interpreted) provide the appropriate means to properly resolve the true nature of multiplication. So the multiplication of 2 numbers requires 2-dimensional interpretation (with a 1st and 2nd dimension applying); the multiplication of 3 numbers would then entail 3-dimensional interpretation (with a 1st 2nd and 3rd dimension applying).

In general the multiplication of n numbers would require n-dimensional interpretation (with a 1st, 2nd, 3rd,....nth dimension applying).

Now - what I refer to as - the Zeta 2 zeros relate to all the dimensions (other than the 1st) which provide the general means for holistically interpreting all such relationships.

So =  x;

Thus 1 – x = 0.

Therefore (1 – x)(1 + x1 + xx+ ....+ x– 1= 0

Now 1 – x = 0 represents the trivial solution (i.e. x = 1), which relates to the 1st dimension and the initial recognition of the independence of all units.

However 1 + x1  + xx+ ....+ x– 1 = 0, provides the equation for establishing the true holistic nature of all higher dimensions.

The simplest possible case (which serves as a holistic template for all others) occurs when n = 2.

So here 1 + x(i.e. 1 + x) = 0; therefore x = – 1.

This is the first of the Zeta 2 zeros and has vitally important role to play.

Basically it serves to express (in an indirect manner) the nature of holistic interdependence in the 2-dimensional case.

Now if we look for the extreme example (of the most highly refined intuitive understanding possible) then – 1 (i.e. the 1st trivial zero) can holistically be understood as representing a pure psycho spiritual energy state (with a complementary interpretation as a pure physical energy state).

So just as anti-matter (when in contact with matter) particles will fuse in a pure physical energy state, likewise this is true of number (which represents the encoded nature of reality in both physical and psychological terms).

Equally all other Zeta 2 zeros can be understood (in their fullest experiential attainment) as representing in holistic terms pure energy states. What this implies is that one can then directly intuit in experience the purely relative nature of an ever increasing number of different frames. This requires therefore great transparency with respect to understanding, where phenomenal rigidity is greatly eroded.

However the Zeta 2 zeros equally play a remarkably important role with respect to our everyday understanding of number (that is not at all well realised).

If we return again to the simplest case of 2, we see that this is identified with a 1st and 2nd dimension that can be holistically represented as + 1 and – 1 respectively.

Now in qualitative terms + 1 simply relates to analytic type understanding (where polar frames are understood as separate). However – 1 represents the unconscious negation of such understanding leading to the directly intuitive realisation (at an unconscious level) of their mutual identity.

Now implicitly such understanding is required to understand the ordinal relationship of 2 members (of a group of 2).

Thus the ordinal identification of 1st and 2nd (with respect to this group of members) implicitly entails corresponding realisation of the first two zeros (trivial and non-trivial).

Likewise the identification of the 1st, 2nd and 3rd (in the context of 3 members) implicitly entails corresponding realisation of the zeros corresponding to n = 3 (with again one trivial corresponding to the root of 1 and the other two non-trivial corresponding to the other two roots).

And in general the ordinal identification of 1st, 2nd, 3rd,....nth (in the context of n members) implicitly entails corresponding realisation of the zeros corresponding to n = n (with again one trivial and the the other n – 1 corresponding to non-trivial solutions).

Thus to put it briefly, the Zeta 2 zeros intimately underlie our everyday analytic appreciation of the ordinal nature of number (as its unrecognised holistic basis). And this unrecognised holistic basis equally implies its unrecognised unconscious basis!

So without implicit interaction of this deepest holistic (unconscious) layer of understanding, the conventional ordinal appreciation of number would simply not be possible.

One important consequence of this is that it demonstrates the merely relative nature of ordinal understanding.
For example we might initially think that the notion of 2nd has an unambiguous identity.

However 2nd (in the context of 2) is distinct from 2nd (in the context of 3) which is distinct from 2nd in the context of 4 and so on!

Thus the notion of 2nd - as indeed all other ordinal number notions - can potentially be given an unlimited number of possible definitions.

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